Skip to main content
SpringerLink
Log in

On Positivity and Stability of Linear Volterra-Stieltjes Differential Systems

  • Conference paper
Positive Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 389))

Abstract

An explicit criterion for positive linear Volterra-Stieltjes differential systems is given. Then new explicit criteria for uniform asymptotic stability and exponential asymptotic stability of positive linear Volterra-Stieltjes differential systems are presented. Finally, a crucial difference between the uniform asymptotic stability and the exponential asymptotic stability of linear Volterra-Stieltjes differential systems is shown.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Gripenberg, G., Londen, S.O., Staffans, O.: Volterra Integral and Functional Equations. Cambridge Univeristy Press, New York (1990)

    MATH  Google Scholar 

  2. Murakami, S.: Exponential asymptotic stability for scalar linear Volterra equations. Differential Integral Equations 4, 519–525 (1991)

    MATH  MathSciNet  Google Scholar 

  3. Naito, T., Shin, J.S., Murakami, S., Ngoc, P.H.A.: Characterizations of positive linear Volterra differential equations. Integral Equations and Operator Theory 58, 255–272 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ngoc, P.H.A.: On exponential asymptotic stability of linear Volterra-Stieltjes differential systems (in preparation, 2009)

    Google Scholar 

  5. Ngoc, P.H.A., Naito, T., Shin, J.S.: Characterizations of postive linear functional differential equations. Funkcialaj Ekvacioj 50, 1–17 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Ngoc, P.H.A., Naito, T., Shin, J.S., Murakami, S.: On stability and robust stability of positive linear Volterra equations. SIAM Journal on Control and Optimization 47, 975–996 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  7. Ngoc, P.H.A., Murakami, S., Naito, T., Shin, J.S., Nagabuchi, Y.: On positive linear Volterra-Stieltjes equations. Integral Equations and Operator Theory (in press) (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ilmenau Technical University, Weimarer Straße 25, 98693, Ilmenau, DE

    Pham Huu Anh Ngoc

Authors
  1. Pham Huu Anh Ngoc
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camí de Vera s/n, 46022, Valencia, Spain

    Rafael Bru  & Sergio Romero-Vivó  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ngoc, P.H.A. (2009). On Positivity and Stability of Linear Volterra-Stieltjes Differential Systems. In: Bru, R., Romero-Vivó, S. (eds) Positive Systems. Lecture Notes in Control and Information Sciences, vol 389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02894-6_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02894-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02893-9

  • Online ISBN: 978-3-642-02894-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation